ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESS CONVOLUTION SEMIGROUPS

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ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESS CONVOLUTION SEMIGROUPS

Let D be a convolution semigroup of random measures or point processes on a locally compact second countable T 2space. There is a topological isomorphism from D into a subsemigroup of product topological semigroup (R , ) N.D is a sequentially stable and D-separable ZH-semigroup, as well as a metrizable, stable and normable Hun semigroup, so it has the corresponding properties. In particular the author has a new and simple proof byZH-semigroup approach or Hun semigroup approach to show that D has property ILID (an infinitesimal array limit is infinitely divisible), and know the Baire types which some subsets of D belong in.